De, Aritra2022-08-292022-08-292022-04https://hdl.handle.net/11299/241375University of Minnesota Ph.D. dissertation. April 2022. Major: Physics. Advisor: Joseph Kapusta. 1 computer file (PDF); xii, 183 pages.The main focus in this thesis is on the phenomenology of heavy-ion collisions, especially hydrodynamic fluctuations and quark-gluon plasma at finite baryon densities. Atoms consist of electrons bound to a nucleus. Inside the nucleus are the subatomic particles - protons and neutrons which are themselves bound state of quarks and gluons. If the energy density and the temperature of the nucleus is made high enough, the quarks are no longer bound in these protons and neutrons. Instead, quarks, antiquarks and gluons become deconfined and form a thermal state called quark-gluon plasma (QGP). Such deconfinement happens in the early universe after the Big Bang. As the universe expands, it cools and quarks get confined into hadrons (protons, neutrons). There are experimental facilities which produce QGP, such as the LHC (Large Hadron Collider) at CERN (Geneva) and the RHIC (Relativistic Heavy Ion Collider) at Brookhaven National Laboratory (New York). Relativistic hydrodynamic simulations have been very successful in explaining the collective behaviour observed in QGP formed in the heavy-ion collision experiments. There are thermal fluctuations in any hydrodynamic system. Study of these fluctuations can be used to extract transport properties of QGP like shear viscosity, bulk viscosity, thermal conductivity etc. Fluctuations are also important in order to detect the presence of the postulated critical point in the QCD (Quantum Chromodynamics) phase diagram. Systematic quantification of these fluctuations in the heavy ion collision simulations is essential to detect the QCD critical point if there is one and that is what has been studied in this thesis. In addition, a new 3D initial state has been proposed for finite baryon densities and, out-of-equilibrium distribution functions have been calculated for finite baryon densities. They have been utilized to perform realistic heavy ion collisions for low energies in anticipation of Beam Energy Scan program at RHIC. Lastly, the stochastic machinery developed was put to work in the context of cosmological inflation to arrive at some novel results.enHydrodynamic fluctuationsNuclear matterParticle correlations & fluctuationsQuark gluon plasmaRelativistic heavy ion collisionsStochastic differential equationsThesis or Dissertation